You have probably seen Formula 1 cars weaving during the warm-up lap and under caution. That's because their tires are engineered for very high temperature and their performance degrades significantly when they are cold.
So do yourself and everyone else a favor and don't do anything stupid like that at performance driving events.
1. Driving events are for performance driving education, not racing.
2. You won't feel any difference in handling in your street tires if their temperature drops.
3. Other drivers around you will thank you.
4. You won't hurt yourself.
5. Your instructor might be willing to ride with you again.
6. You'll save yourself some money for real tires.
Maybe most importantly, you'd be able to scream at the top of your lungs: "I am not a doofus!"